ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and Fran├žois-Xavier Coudert at CNRS / Chimie ParisTech.
If you use the software in published results (paper, conference, etc.), please cite the corresponding paper (J. Phys. Condens. Matter, 2016, 28, 275201) and give the website URL.

ELATE is open source software. Any queries or comments are welcome at

Summary of the properties

Input: stiffness matrix (coefficients in GPa) of SiC (Materials Project id mp-11714)

       490      104       50        0        0        0  
       104      490       50        0        0        0  
        50       50      533        0        0        0  
         0        0        0      158        0        0  
         0        0        0        0      158        0  
         0        0        0        0        0      193  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 213.44 GPaEV = 437.9 GPaGV = 189.07 GPaνV = 0.15807
ReussKR = 213.43 GPaER = 429.31 GPaGR = 184.29 GPaνR = 0.16475
HillKH = 213.44 GPaEH = 433.62 GPaGH = 186.68 GPaνH = 0.1614

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
158 GPa 158 GPa 193 GPa 386 GPa 486.49 GPa 640.51 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 396.21 GPa 524.58 GPa 1.5501 TPa–1 1.5854 TPa–1 158 GPa 228.43 GPa0.0841750.25791Value
Anisotropy 1.324 1.0228 1.446 3.0640Anisotropy
Axis 0.6940
0.2845
0.6614
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.1221
0.6965
0.7071
0.0000
0.0000
1.0000
0.6916
-0.0002
0.7223
Axis
-0.7660
0.6428
0.0000
0.1221
0.6965
-0.7071
0.1736
0.9848
-0.0000
0.7223
-0.0004
-0.6916
Second axis

Spatial dependence of Young's modulus



Young's modulus in (xy) plane

Young's modulus in (xz) plane

Young's modulus in (yz) plane

Spatial dependence of linear compressibility



linear compressibility in (xy) plane

linear compressibility in (xz) plane

linear compressibility in (yz) plane

Spatial dependence of shear modulus



Shear modulus in (xy) plane

Shear modulus in (xz) plane

Shear modulus in (yz) plane

Spatial dependence of Poisson's ratio



Poisson's ratio in (xy) plane

Poisson's ratio in (xz) plane

Poisson's ratio in (yz) plane